An integrated reliability study of the containment vessel of a nuclear power plant is presented. The focus is on features of the seismic and accident behavior that may affect adversely the containment safety role. The behavior is described probabilistically under a range of accident and seismic conditions extending far beyond design levels. The individual effects of seismic and accident events are analyzed, as well as the coupling of those effects for the various possible timings of the causative events. Reliability estimates are obtained by combining probabilistically described damage with a probabilistic description of the causative events. A large number of uncertainties are included, and the final reliability estimates reflect the total uncertainty—including the statistical component—faced by the safety analyst.